A word having two opposite meanings is called a contranym or a contronym or an antagonym.

Many of the examples below are taken from Enjoy your English! by Nick Renton.

Some of the pairs could more accurately be described as near-opposites.

bill: a banknote (an asset)
bill: a request for payment (a liability)

citation: words relating to an award for good behavior
citation: words relating to a penalty for bad behavior

cleave: to come apart
cleave: to adhere

clip: to cut off (hair, wool and so on)
clip: to fasten together

dust: to remove dust
dust: to sprinkle with dust (as when taking fingerprints)

fast: moving quickly
fast: staying fixed in position

fine: of excellent quality
fine: of barely acceptable quality

hold up: to support or sustain
hold up: to hinder or delay

impregnable: unable to be taken by force
impregnable: able to be filled

lease: to rent out (as lessor)
lease: to hire (as lessee)

left: remaining
left: having departed

let: to hinder
let: to allow

lift a levy: to increase the rate of a levy
lift a levy: to abolish a levy

moot: arguable
moot: not worthy of argument

overlook: to watch over
overlook: to fail to notice

oversight: watchful control
oversight: a failure to notice

put out: to extinguish
put out: to produce

rent: to let out (as landlord)
rent: to hire (as tenant)

sanction: to permit
sanction: to impose a penalty

screen: to hide from view
screen: to show publicly

seed: to add seeds to something
seed: to remove seeds from something