The short answer, "re-enacting" is the same as acting, but it is a term that denotes acting out a historic event, or acting as someone (or type of person) from a particular historic context for educational purposes. For example, a Viking re-enactor is someone who dresses as a Norse raider from the 8th to 10th century A.D. and portraying what a Viking would do, either through theatrical battle displays or by displaying the skills and crafts practiced by the Norse people of that time.
The longer answer is, re-enacting is an art that tens of thousands if not hundreds of thousands of people have taken up across the globe. There are re-enactors that display the lifestyles, art, crafts, or battles, of time frames from as early as the Stone Age, right up to the current wars going on in the world today. Most re-enactors put a great deal of time researching their costumes (garb) and practicing the crafts that were practiced by the historic figures or culture the re-enactor is emulating. Some re-enactors can become involved with re-enacting different times or cultures as well. Other re-enactors try to broaden their scope and re-enact a broader time and/or cultural base, and include items from different eras and cultures together in one display. To build on the previous example, a "Dark Age" re-enactor may include items or personification from the Carolingian (Early Franks/France under Charlemagne), Norse, or even Byzantium cultures as well as including items form all of these areas (and/or more) from the 5th to 10th centuries A.D. Other re-enactors are very focussed and may be very specific as to their time frame and culture. For example, re-enactors who focus on England in 1066 A.D., would focus on re-enacting the cultures and items from or near the time frame of the Norman invasion of Saxon England.
It is possible even to re-enact fantasy or science fiction, although these types of re-enactors tend to be less common, and really people that prefer fantasy or science fiction tend to be drawn to live action role playing rather than re-enacting. How is live action role-playing different from re-enacting? That is mostly a matter of opinion, but I tend to draw the line at if the events are completely unscripted, it would be live action role playing, if the events are recreating a scene or theme from a fantasy or science fiction source with guidelines as to the course of action, I could consider it re-enacting. On the whole this web site will be dedicated more to historic re-enacting. Some mention of fantasy or science fiction re-enacting may be made, and should the occasion arise, articles about science fiction or fantasy re-enacting may be included on this web site.
There are many different approaches to re-enacting, and one must always remember that there is no correct or incorrect way of re-enacting, only different approaches. One of the biggest differences in approach lies in the method of construction of costumes (garb). Some re-enactors take the approach of just trying to create a realistic look to their costumes, and are less concerned with the materials they use. Other re-enactors are very particular and will only use materials based on or are the same as those that have been found in archaeological finds of their chosen time frame and culture, and even go so far as to select fabrics of the same or similar weave to those found in archaeological finds. Another stylistic difference between re-enactors is the level of extrapolation used. Some re-enactors use solely items or materials based exclusively on archaeological finds, while other re-enactors take more of a stance that while this item or material was not find in that area in that time frame, said item or material was found in surrounding areas, or near that time frame, or alternatively using a material or item that could have plausibly existed in their chose time frame or culture. Of course as soon as the term plausible is applied, one needs to deal with the sometimes widely differing opinions on what is or isn't plausible.