1. To propel someone or something forward by pressing or leaning on them or it. In this usage, a noun or pronoun is used between "press" and "forward." We need to press this part forward so it lines up with the rest of the machine. Someone pressed me forward when the captain asked for volunteers.

2. To continue moving forward, especially in spite of a physical impediment of some kind. We kept pressing forward through the thick jungle foliage. I know everyone is tired, but we should press forward and get to camp before it gets too dark.

3. To continue making progress (in something), especially in spite of some kind of difficulty, setback, problem, etc. The loss of our chief researcher is tough, but we're going to press forward with our project nonetheless. I just hope the two governments keep pressing forward with discussions for a peace agreement.