The meaning of the second half of this famous quote is fairly obvious; science is not infrequently compared to light (e.g., Carl Sagan’s "Science as a Candle in the Dark”), dispelling ignorance and illuminating a more accurate vision of Reality (what's actually going on in the universe). Which is to suggest that Einstein considered any belief system/religion which rejected the findings and conclusions of scientific investigation a pointless lurch in the darkness of delusion.
The first half of this quote is a little more enigmatic. It is well known that Einstein had little patience for anachronistic belief systems (he was born to Jewish parents and did have a religious phase when he was 11, but by the time he was 13 he had been exposed to enough science to refuse his own Bar Mitzvah). In the same letter in which he wrote "Science without religion is lame…." he also wrote "The word ‘God’ is for me nothing more than the expression and product of human weaknesses, the Bible a collection of honorable, but still primitive legends which are nevertheless pretty childish. No interpretation no matter how subtle can (for me) change this.” What then could he have meant by "science without religion is lame"? In what way does science need religion?
Words like “injured”, “impaired”, “ineffectual”, and “inept”, are found in most definitions of “lame”. How could a lack of religion have a debilitating effects on science? Clearly Einstein was talking about a different kind of religion. Although we use the word “religion” primarily to describe organized (and usually hierarchical) belief systems, the etymology of the word reveals that it is a combination of the Latin word ligare (to connect) and the prefix re (i.e. re-ligare, meaning “to reconnect”). Perhaps Einstein was alluding to the possibility that science itself has an inherent religious aspect, that science is itself a profoundly important mode of “reconnecting” our consciousness (and therefore our being) to what’s actually going on in the universe, and that scientific reconnection to the source of our existence at both a cosmological (the big bang) and a biological (evolution) level has spiritual significance.
“The most beautiful thing we can experience is the mysterious. It is the source of all true art and all science. He to whom this emotion is a stranger, who can no longer pause to wonder and stand rapt in awe, is as good as dead: his eyes are closed.” Einstein
Although religion is not mentioned in the last quote, the superlative value Einstein places on the experience of ‘awe’ and ‘wonder’ invoked by the Great Mystery (i.e., why is there something rather than nothing, and why does that something unfold energy into matter into life into mind into wonder?) sounds very much like the experience of ‘reconnecting’ to the source of Being; a ‘religious experience’ (found in many traditions, including Christianity) that beckons us to experience ‘now’ (the only moment which actually exists) with a mind clarified and open, empty of dogma and judgment, drifting on the silent water as the starry night turns above us. Science is knowing that the earth moves, Religion is feeling it.