Yea there are limitations, but you'll probably never get close to them (connections is not the same as connecting or incomming connections, a connection is something that has happned and is established and that number is significantly higher than other states. @corsiKa gave a good quote on the number of connected sessions you can have.)
Here are some useful commands:
# Shows some general useful information,
ulimit -a
# if not, here are some other places to look
# maximum files:
cat /proc/sys/fs/file-max
# maximum filedescriptors:
cat /proc/sys/fs/file-nr
# maximum backlog of unaccepted clients:
cat /proc/sys/net/core/somaxconn
# And number of threads to run at once:
cat /proc/sys/kernel/threads-max
What limits how many open You->Them
connections is basically how many local ports you have availible and assigned as your pool, you can find this information in:
sysctl net.ipv4.ip_local_port_range
There's also a "buffert" on incoming ports that limits how many clients you can simultaionsly have connecting to you, find this information here:
sysctl net.ipv4.tcp_max_syn_backlog
sysctl net.core.netdev_max_backlog
Also, find a complete description here: Increasing the maximum number of tcp/ip connections in linux