When you experience this behavior, it means that you are probably using outline levels for your project tasks and that one or more of the parent rows (also called summary rows) has a Constraint Date applied to it with a Constraint Type of 'Start On or After'. When a summary task has this Constraint Type applied, the Constraint Date is being applied to activities below it.
To free all activities from this constraint, Insert > Column > Constraint Type. Change ALL summary rows' Constraint Types to 'As Soon As Possible'. These summary rows should be easy to spot because they are in bold. Your activities should be free to move anywhere on the timeline (unless they are dependent on another activity and a link is defined).
This setting may have been inadvertently applied if you grabbed multiple bars on the timeline graph and dragged them. Selecting the bars would have included summary tasks and would have changed the Constraint Type. To avoid this in the future, before selecting and dragging the bars, View > deselect Summary Bars (to hide them temporarily). Once you have completed the move, you can go back to showing the summary bars.