Involvement in prayer benefits both those who pray, and those who are prayed for.
Personally, prayer increases intimacy with God, helps develop a healthy dependence on God, and changes primarily our hearts, rather than God. Additionally, when we pray consistently for change that honors God, seeing God affirmatively answer our prayers encourages our faith.
We bless missionaries when we pray because we are actually co-laboring to break up hard spiritual ground. Missionaries have told many stories of specific times when it was clear to them that people had prayed at a specific time, or stopped praying. A particular spiritual breakthrough occurs, or borders are crossed with possessions that normally would be caught and removed in customs lines. Money and supplies last longer than they should have.
On the other hand one missionary couple in Italy went through a particularly tough term and could sense that their home church had stopped praying consistently for them. They later found out that during that specific 18-month period, the church became consumed in fighting about a doctrinal issue and ceased praying as fervently.
It’s our great privilege to pray fervently for missions!