Betting with a drawing hand is a significant and strategic bet.
Also known as semi-bluffing, you both disguise the hand you have, as well as place your opponent(s) into a position of determining if they will continue.
While holding a 56off, and weak or no action in front of you, a board of Jc 4d 3s offers an ideal semi-bluff opportunity. A bet or raise here could force any pair less than jacks to fold. J 10 or worse may pause, and possibly not commit any more money to the pot because of your bet, giving you a chance to draw out on 4th and 5th street if you decide not to commit any more money to the pot. Your semi-bluff will possibly place him into a calling mode, rather than a betting mode, leaving you in the drivers seat.
As far as odds go, you are behind in this J 10o scenario - you'll win only ~ 34% of the time if it comes to a showdown - but, aggressive betting on 4th and 5th street, can get someone to fold, even with the best hand.
In Chad's straight only scenario, with the turn coming, you are a little better than a coin flip to win in a showdown at the river.