Because of the length required to write out an entire crochet pattern in long hand, common abbreviations are used in nearly all patterns. Take, for example, this row of a pattern:
Double crochet in the 4th chain from the hook, then chain 1, skip 1 chain, make 1 double crochet in each of the next 4 chains. Chain 1, skip 1 chain, and make 1 double crochet in each of the next 4 chains until reaching the end of the row. Finish by chaining 1, skipping 1 chain, and making 1 double crochet in each of the last 2 chains. Lastly, chain 3, and turn.
Versus the same row of instructions, in shorthand abbreviations:
Dc in 4th ch from hk, *ch 1, sk 1 ch, 1 dc in ea of next 4 ch. Rep from * across, ending ch 1, sk 1 ch, dc in ea of last 2 ch, ch 3, turn.
Though it may appear daunting at first, in the end, shorthand patterns save experienced crocheters time, and even money, because pattern books will cost less when they are shorter.

The common crochet abbreviations:
BLO
Back loop(s) only
BPdc
Back Post double crochet(s)
DBhdc
Back Post half double crochet(s)
CC
Contrasting Color
ch(s)
chain(s)
dec
decrease
dc
double crochet(s)
ea
each
Ex sc
Extended single crochet(s)
FLO
Front Loop(s) Only
FPdc
Front Post double crochet(s)
FPtr
Front Post treble/triple crochet(s)*
hdc
half double crochet(s)
hk
hook
inc
increase
lp
loop
MC
Main Color
rep
repeat
Rnd(s)
Round(s)
sc
single crochet(s)
sk
skip
sl st
slip stitch
sp(s)
space(s)
st(s)
stitch(es)
tr
treble/triple crochet(s)
YO
Yarn Over
* Note that triple crochet and treble crochet mean the same thing, and are used interchangeably, with triple crochet being the more common term.
Sources:
Crochet For Today, Anne Child
Crocheting in Plain English, Maggie Righetti