Both are PAST TENSE. The first ("I worked") is the SIMPLE PAST. It can mean the following:
"I completed some amount of work" (e.g., "I worked on my report for an hour.").
"I went to my place of work" (e.g., "I worked Monday - Friday this week.").
"I used to work regularly" (e.g., "When I was twenty, I worked at McDonald's.").
"I gave an effort" (e.g., "I worked on my relationship with Susan, but she left me anyway.").
The second ("I did work") is the EMPHATIC PAST (which is a "mood" and not a tense). It can mean the following:
"Someone thinks I didn't work, but that is untrue."
In this case, "work" is a verb and the mood of the verb is EMPHASIZED by the auxiliary verb (helping verb) "did".
This sentence ("I did work.") can ALSO be interpreted differently:
"I did [some] work." or "I completed some amount of the work."
Ex.: "I did work on Joan Rivers face and lost my job as a surgeon."
In this case, "did" is the main verb, and "work" has become a noun (the thing "done").