Can anyone explain me the difference between "walks," "walked," and "will walk"?
Martha loves exercising so she walks/walked/will walk everywhere she goes.
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Those are three different tenses.
walks (third person singular present tense; regular action or habit)
— She walks everyday.
walked (past tense; completed action on a specific time)
— She walked yesterday.
will walk (future tense; planned stuff to do in the future)
— She will walk within two days.
walks - present simple tense (3rd person singular)
will walk - used to refer to future time (often called the future tense)
walked - past simple tense (it's not grammatical in your sentence, since Martha loves exercising is in the present tense.)
For more information, I highly suggest you read a basic grammar site about verb tenses. You can start here on this page at the English Club.