It is important to know the difference between a true sentence and a sentence fragment, because readers expect complete sentences in your novel, unless you are writing as a 1st person narrator with a distinctive speech pattern. It is also important to know what a compete sentence is -- a true sentence -- because you need to know to conclude it with a full stop (period) or a semicolon or, if it is not complete, with a comma. 

Consequently, it is also important to be able to identify a finite verb, because it is the key to being able to identify what IS and is NOT a true complete sentence.

A true complete sentence must contain a finite verb and subject. 

The subject could be a thing, a person or a represented by a pronoun.  It could be ‘the man’, ‘mountains’, ‘Mister Smith’, ‘joy’,  ‘’it’, she’, or ‘I’. The subject could even be a longer phrase: The man who warned me about pickpockets.

The term 'finite verb' simply means that the verb is limited in some way… by being in past or present tense or by being pinned to one person or several.

The infinitive of a verb has no limits: to swim, to fly, to think, to eat … these infinitives offer no clue to whether one person is doing it or ten people, or whether it is being done right now, ten years ago or maybe in the future.
In the same way the type of verb called a participle is not a finite verb  –  words such as ‘swimming, driving, or loving give no clue as to when the action occurred or who is doing it.

If you put the finite verb ‘was’ in front of, say, ‘swimming’, we can instantly tell that ONE person did this swimming some time in the past.  If we put the finite verb ‘are’ in front, then we know immediately that the action is taking place right now and that either a number of people ARE doing it… or else the person we are talking to happens to be doing it … ‘you are swimming’.

When we pin down a verb with an ending it becomes a finite verb.  In English certain forms are tied to specific  pronouns – we call it ‘person’ – 1st person, 2nd person, 3rd person and we indicate whether it is singular or plural.
1st Person   singular – I walk
2nd person  singular – you walk
3rd person singular  –  he walks

1st person plural   -     we walk
2nd person plural  -     you walk
3rd person plural  -  they walk

To show that an action happened in the past … either years or just seconds ago … the finite verb takes an ending that makes this clear.
I walked, you walked, she or he walked, we walked, you (plural) walked, they walked.
In English, obviously, the same ending is used for all past tense verbs.  In many other languages, however, the speaker needs to learn a different ending for each person in past tense.

So, to reiterate, when we put a subject with a finite verb, we get an independent clause, which is often a complete sentence.
It can be very short but the combination makes it a true sentence.
  Eg. John sank.
Bill shouted.
Jim edits.
The man who goes to the bar all day is a heavy drinker.
Smiling is a sure sign if happiness.
Shoppers of a certain kind will line up overnight for sales.     

Be`warned: Collections of words that are missing either a finite verb or a subject are not true sentences. They are then called sentence fragments.
Eg: Swimming, the best of exercise [no finite verb]
Walking down the road, whistling an old song. [no subject] 

If you would like to test your understanding of what is a complete sentence, TRY THIS SENTENCE WORKSHEET