Application developed in C may use dynamic libraries (.so files) to reuse the
common functions/symbols in the binary. If the library bumped its soname (
changed major version, API/ABI incompatibility), application that depends on
it may not run.
Some of the libraries changed the soname version between CentOS
6 and CentOS 7.

From your CentOS 6 packages, following libraries changed soname:

libMagickCore.so.2 from ImageMagick changed to libMagickCore.so.5
libMagickWand.so.2 from ImageMagick changed to libMagickWand.so.5
libanonymous.so.2 from cyrus-sasl-lib changed to libanonymous.so.3
libarchive.so.2 from libarchive changed to libarchive.so.13
libbind9.so.80 from bind-libs changed to libbind9.so.90
libboost_filesystem-mt.so.5 from boost-filesystem changed to libboost_filesystem-mt.so.1.53.0
libboost_filesystem.so.5 from boost-filesystem changed to libboost_filesystem.so.1.53.0
libboost_program_options-mt.so.5 from boost-program-options changed to libboost_program_options-mt.so.1.53.0
libboost_program_options.so.5 from boost-program-options changed to libboost_program_options.so.1.53.0
libboost_system-mt.so.5 from boost-system changed to libboost_system-mt.so.1.53.0
libboost_system.so.5 from boost-system changed to libboost_system.so.1.53.0
libcamel-1.2.so.19 from evolution-data-server changed to libcamel-1.2.so.43
libcrammd5.so.2 from cyrus-sasl-md5 changed to libcrammd5.so.3
libcryptsetup.so.1 from cryptsetup-luks-libs changed to libcryptsetup.so.4
libdigestmd5.so.2 from cyrus-sasl-md5 changed to libdigestmd5.so.3
libdns.so.81 from bind-libs changed to libdns.so.100
libdricore9.2.0-devel.so.1 from mesa-dri-drivers changed to libdricore9.2.2.so.1
libdrm_nouveau.so.1 from libdrm changed to libdrm_nouveau.so.2
libebackend-1.2.so.0 from evolution-data-server changed to libebackend-1.2.so.6
libebook-1.2.so.10 from evolution-data-server changed to libebook-1.2.so.14
libecal-1.2.so.8 from evolution-data-server changed to libecal-1.2.so.15
libedata-book-1.2.so.8 from evolution-data-server changed to libedata-book-1.2.so.17
libedata-cal-1.2.so.10 from evolution-data-server changed to libedata-cal-1.2.so.20
libedataserver-1.2.so.14 from evolution-data-server changed to libedataserver-1.2.so.17
libgdbm.so.2 from gdbm changed to libgdbm.so.4
libgmp.so.3 from gmp (required by NonCentOS signed package(s):mpfr ) changed to libgmp.so.10
libgnutls.so.26 from gnutls changed to libgnutls.so.28
libgnutlsxx.so.26 from gnutls changed to libgnutlsxx.so.28
libgphoto2.so.2 from libgphoto2 changed to libgphoto2.so.6
libgphoto2_port.so.0 from libgphoto2 changed to libgphoto2_port.so.10
libgs.so.8 from ghostscript (required by NonCentOS signed package(s):netpbm-progs ) changed to libgs.so.9
libgssapiv2.so.2 from cyrus-sasl-gssapi changed to libgssapiv2.so.3
libgstbasevideo-0.10.so.0 from gstreamer-plugins-bad-free (required by NonCentOS signed package(s):totem ) changed to libgstbasevideo-0.10.so.23
libgstphotography-0.10.so.0 from gstreamer-plugins-bad-free (required by NonCentOS signed package(s):totem ) changed to libgstphotography-0.10.so.23
libgstsignalprocessor-0.10.so.0 from gstreamer-plugins-bad-free (required by NonCentOS signed package(s):totem ) changed to libgstsignalprocessor-0.10.so.23
libicudata.so.42 from libicu changed to libicudata.so.50
libicui18n.so.42 from libicu changed to libicui18n.so.50
libicuio.so.42 from libicu changed to libicuio.so.50
libicule.so.42 from libicu changed to libicule.so.50
libiculx.so.42 from libicu changed to libiculx.so.50
libicutu.so.42 from libicu changed to libicutu.so.50
libicuuc.so.42 from libicu changed to libicuuc.so.50
libini_config.so.2 from libini_config changed to libini_config.so.3
libisc.so.83 from bind-libs changed to libisc.so.95
libisccc.so.80 from bind-libs changed to libisccc.so.90
libisccfg.so.82 from bind-libs changed to libisccfg.so.90
libkdb5.so.6 from krb5-libs (required by NonCentOS signed package(s):libgssglue ) changed to libkdb5.so.7
libkpathsea.so.4 from kpathsea changed to libkpathsea.so.6
liblogin.so.2 from cyrus-sasl-plain (required by NonCentOS signed package(s):kdepim ) changed to liblogin.so.3
liblwres.so.80 from bind-libs changed to liblwres.so.90
libmysqlclient.so.16 from mysql-libs changed to libmysqlclient.so.18
libnetsnmp.so.20 from net-snmp-libs changed to libnetsnmp.so.31
libnetsnmpagent.so.20 from net-snmp-libs changed to libnetsnmpagent.so.31
libnetsnmphelpers.so.20 from net-snmp-libs changed to libnetsnmphelpers.so.31
libnetsnmpmibs.so.20 from net-snmp-libs changed to libnetsnmpmibs.so.31
libnetsnmptrapd.so.20 from net-snmp-libs changed to libnetsnmptrapd.so.31
libnm-glib.so.2 from NetworkManager-glib changed to libnm-glib.so.4
libnm-util.so.1 from NetworkManager-glib changed to libnm-util.so.2
libopenjpeg.so.2 from openjpeg-libs changed to libopenjpeg.so.1
libpackagekit-glib2.so.12 from PackageKit-glib changed to libpackagekit-glib2.so.16
libpcre.so.0 from pcre (required by NonCentOS signed package(s):nginx ) changed to libpcre.so.1
libplain.so.2 from cyrus-sasl-plain (required by NonCentOS signed package(s):kdepim ) changed to libplain.so.3
libpoppler-glib.so.4 from poppler-glib changed to libpoppler-glib.so.8
libpoppler-qt4.so.3 from poppler-qt4 changed to libpoppler-qt4.so.4
libpoppler.so.5 from poppler changed to libpoppler.so.37
libproxy.so.0 from libproxy changed to libproxy.so.1
librpm.so.1 from rpm-libs changed to librpm.so.3
librpmbuild.so.1 from rpm-libs changed to librpmbuild.so.3
librpmio.so.1 from rpm-libs changed to librpmio.so.3
libsasl2.so.2 from cyrus-sasl-lib changed to libsasl2.so.3
libsasldb.so.2 from cyrus-sasl-lib changed to libsasldb.so.3
libtasn1.so.3 from libtasn1 changed to libtasn1.so.6
libtiff.so.3 from libtiff changed to libtiff.so.5
libtiffxx.so.3 from libtiff changed to libtiffxx.so.5
libudev.so.0 from libudev changed to libudev.so.1
libverto.so.0 from krb5-libs (required by NonCentOS signed package(s):libgssglue ) changed to libverto.so.1
libvpx.so.0 from libvpx changed to libvpx.so.1
libweather_ion.so.4 from kdebase-workspace-libs changed to libweather_ion.so.6
libxcb-icccm.so.1 from xcb-util changed to libxcb-icccm.so.4
libxtables.so.4 from iptables changed to libxtables.so.10

We checked the requirements in Non-CentOS signed packages, but for the non
rpm-packaged binaries, you should check the compatibility list yourself
by using e.g. ldd <binary> command.
If some of your application uses the library on the list above, you will
need to rebuild such package/application against new library.
CentOS applications available on the CentOS 7 will handle
these bumps automatically by the update/migration to new CentOS
as they were already built against these libraries.