Mass Effect: Andromeda takes place just before the Reaper invasion featured in Mass Effect 2. The Tempest embarks on a 600 year journey to the Andromeda Galaxy. Its main mission is to find a new world for humanity to colonise and thrive.
Even though the game does start in the middle of the original Mass Effect trilogy it technically doesn't officially get going until centuries after the end of Mass Effect 3. This however doesn’t mean that Andromeda will be a huge departure from the original series. The developers have promised there will be nods to the previous games throughout Andromeda, there will be a lot of fan service for veteran players of the series to scope out.
Players of the previous Mass Effect games will feel right at home though as the Tempest is Andromeda’s answer to Shepard’s space ship the SSV Normandy. You will also be able to explore planet surfaces in the NOMAD, an upgraded version of the M35 Mako from the original trilogy.
So as you can see, there are several similarities and links between Mass Effect: Andromeda and the previous Mass Effect trilogy.