for some reason im getting this error and i dont know what to do

i just moved my site to a dedicated server i thot it was going to be better but if this keeps up like this my wallpaper website will keep crashing

help, how can i stop this error from coming back again

UPDATE

ok i found the answer to this. i have red hat fedora core server so i logged in as root and send these commands:

Edit my.cnf file with your favorite editor, im using nano you can use vi if you prefer
nano /etc/my.cnf


now add this line under [mysqld] section
set-variable=max_connections=250


save the changes and then restart mysqld server:
/etc/init.d/mysqld restart


Done