'It may be said of one who is contented in a Christian way that he is the most contented man in the world, and yet the most unsatisfied man in the world'.
Being content has connotations of being happy with second-best, but that's not what Burroughs is on about. Contentment is bound up with knowing God is in control, and so one can be contented 'if he has but bread and water'. Yet at the same time there is a sense in which we are to be dissatisfied in the world; 'that is, those things that will satisfy the world, will not satisfy him.'
That's a brilliant observation I reckon: the two sides of contentment, finding a satisfaction in any situation, yet not being satisfied with it alone, for only God will satisfy. Another helpful thing Burroughs points out is that Christian contentment 'is not opposed to all lawful seeking for help in different circumstances, not to endeavouring simply to be delivered out of present afflictions by the use of lawful means'. That is, in situations of suffering it is not ungodly to ask God to deliver us from them and to keep in mind that he may well do that. He says that's what marks true Christian contentment out from glib stupidity.
I reckon that's something of what Paul is talking about in Philippians - being content in every situation, yet still a striving forward, a longing for the inheritance of God.