The SMS protocol (which is used for texting) has a 140 octet limit (an octet is a group of 8 bits). Since text characters are 7 bits, the 140 octets is 1120 bits, and 160 7 bit characters are 1120 bits.
Some texting apps send larger texts as SMS files, with the text being the address the recipient presses to get the text file, some send a large text as multiple 160 character texts. Or you can use Hangouts, IRC, email or other messaging apps that don't use SMS.
(The problem is that SMS was developed for pocket pagers, which seldom needed more than 140 characters. Stuff like "I'm on the way home", or "meet me at Joe's" or "call me". The industry decided to use SMS for texting, instead of designing some other protocol that the whole industry could agree on. (Apple still doesn't agree on SMS - iMessage and SMS aren't compatible.) Getting the whole electronics industry to agree on a standard makes herding cats look simple. (I've been involved with a few standards committees. Three year olds fighting in a sandbox are more polite.)