Watch Your Mouth!
Be careful what you say.

It would be difficult to literally watch one's mouth, but watch also means to control or to keep it out of trouble - "I need to watch my kids" means I need to take care of them. Here, watch your mouth means to keep it under control and therefore to be careful of what you say. This is said to someone who has said something bad or profane or said to someone as a warning.

"The boss is here, we'll have to watch our mouths."

"Damn it, I forgot my homework!"

"Watch your mouth!"

A Bird in the Hand Is Worth Two in the Bush
Be content with what you have or you may lose everything.

What you have is more valuable than what you might get. In these case a hunter has already caught one bird. The hunter sees two more birds in the bush - two is better than one! In order to capture those birds, the hunter would have to drop the bird that is already caught. The hunter might not be able to catch them and will have nothing. The idiom can also be shortened to "a bird in the hand".

"Even though the money isn't very much, I should take the job because a bird in the hand is worth two in the bush."

"Should we accept their offer or go to court?"

"Let's take the bird in the hand."

Uncharted Waters
A new place or situation.

A chart is another name for a map and waters refers to the sea. "Uncharted waters" refers to a place where no one has traveled and put on a map. A traveler is leaving the known world and entering the unknown. Today, this is generally used to describe a person being in a new and unfamiliar situation. 

"The brave explorer was entering uncharted waters."

"I haven't been single in a long time. It's uncharted waters for me."

Absence Makes the Heart Grow Fonder
Being away from someone or something you love makes you love them more.

In English, as in many languages, the heart represents love. Saying that the heart is fond of something means that the person (who owns the heart) is fond of something. In this picture, a heart is talking to his loved one on the phone.

"I can't wait for my girlfriend to come back. Absence makes the heart grow fonder."

"I really miss my hometown. I guess absence makes the heart grow fonder."

Deep Pockets
Having a lot of money.

The idiom implies that people or businesses with deep (large) pockets are able to carry a lot of money. They probably don't actually keep it all in their pockets, though.

"They can afford this house because they have deep pockets."

"The company didn't do well this year, but it has deep pockets so it'll be fine."

*Sometimes the expression "Short arms and deep pockets" will be used to describe someone with a lot of money, though rarely uses it - he or she can't reach into his or her pockets.

Cash Cow
A product or business that easily makes a lot of money.

The idiom imagines a cow which produces money instead of milk. 
The cow requires little money or effort, but continues to generate money.

"This restaurant is a cash cow. Customers keep coming day after day."

"This smart phone is the company's cash cow. It is so popular!"