He has lots of things going on at once.

1. He has the biggest concrete pour of his life going on, that he cannot be there for, due to other commitments, this led him to being fired, and was the subject of one set of phone calls.

2. Regardless he is a very proud and professional and wants to see the concrete pour go perfectly. He is therefore talking his second in command / replacement, through all the things he needs to do to ensure it is a success. This is the course of a second set of phone calls, including calls to other people involved in the pour.

3. He is about to visit the mother of his unborn child, a woman he had a one night stand with, who has gone into labour, he is phoning the hospital to for status updates. This is a third set of phone calls, and also the reason he is driving in the first place.

4. He has told his wife about his infidelity and the fact he is the father to another woman's child. His marriage is severely strained by this news. This is a fourth set of phone calls between Locke and his wife.

5. He is also talking to his son about how he wont be able to see the football match tonight. This is a fifth set of phone calls.

Out of universe he needs to have people to have dialogue with. Otherwise it is just Tom Hardy driving, not really talking (see Mad Max: Fury Road for that).
The different types of calls and the reasons for them give Hardy the chance to show a differing range of emotions, from professional man in control of everything, to a father trying to do the right thing even though it will cost him everything, to husband trying to do the right thing by his wife and marriage.

I loved this film for that fact, the fact it showed Hardy's range when he really had no one else to act against, just voices on the phone. He had to carry every single one of those scenes and nail the required emotion.