When we pray the silent Amidah (the "standing" prayer), we stand straight with our feet close together. As the Shulchan Aruch says, "One next to the other, as though they were but one," in order, it explains, to be like the angels.
We know that angels stand with their legs straight thanks to Ezekiel's vision of the heavenly chariot. The prophet recorded: "The legs of each were a single rigid leg." Rashi explains that angels do not have joints; their legs do not bend. Since they are always engaged in serving God, they have no need to sit, lie down or rest; hence no knees or ankles are required.
The late atheist, Christopher Hitchens, cited the fact that our knee joints wear out as we grow older as one of those imperfections about the world that make it hard to believe in a wise, benevolent Creator.
The idea behind the angelic comparison is perhaps to transcend this aspect of the human condition and focus single-mindedly on serving God when we pray.