Dogs are kept in a "kennel", often for long periods of time. There is usually a shelter of some kind (protection from the rain), and the area is fenced so that the dogs cannot leave and larger animals cannot enter. The fence (or cage-like structure) is the major feature of a kennel. Kennels can be big or small. .
Another term you will hear is "doghouse". The term refers only to a small structure often in the shape and appearance of a small house. It has one room, a roof, four walls, an opening used as a door, and possibly a window. The doghouse can be very simple or very complex. Note that I have not mentioned a fence. The existence or absence of a fence has nothing to do with the term "doghouse". A fenced kennel, for example, may have a doghouse. Often the doghouse is in the backyard, and the dog can enter or leave whenever he wants to.
to be in the doghouse with = to be in trouble with someone
If a husband comes home drunk, his wife may not let him enter the home. Where is he going to sleep? He could go to a hotel, or perhaps he will sleep inside the doghouse. I have never heard of this happening in real life. It sometimes happens in comedies about marital problems.
(1) She is in the doghouse with the boss. She came to work late and parked her car in his parking space. Now the boss is angry with her.
)2)He is in the doghouse his girlfriend. She is angry because he forgot her birthday.