When ties are used to connect quarter notes and eighth notes as in the following two examples, an "off the beat" feel is created. This is called syncopation. When a chord change is anticipated by half a beat, as you can see it is in these examples by the ties across the bar lines, it is described as giving the rhythm a push.
This example uses both rests on the beat and ties on the beat to create syncopation. Notice the use of the first finger across the 3rd and 4th strings at the 2nd fret.
In the following example, the first finger plays both the 3rd and 4th strings. Instead of playing on the tip, the last segment of the finger is flattened across both strings. This technique is very common in Rock guitar playing.
This symbol is called common time. It means exactly the same as *. The following example uses the common time signature.