It really depends on the context. For plenty purposes, pretty much anything that indicates mutual agreement can be legally binding. E.g. if you call a company to order something, you enter a contract without anything written down at all, and it comes down to "but can you make a convincing case this actually happened as you say it did". Business deals can be made over email. etc. In any such cases, the digital signing services like DocuSign just add another way of documenting agreement. (and presumably people think it's clearer proof or more convenient or ... - it's an interesting question what a court would make out of whatever DocuSign records about a signature)
For other things, there are stricter legal standards of what kind of form of agreement is required, and only then they don't work. I've mentioned this example here a few times, but recently a German grocery delivery startup fell into the trap of using DocuSign for their work contracts. You can enter work contracts just fine with it, but specific clauses in work contracts require paper signature (or a strong cryptographic digital signature), so suddenly the contracts they had intended to be temp contracts were permanent contracts.
(I believe DocuSign also offers the "proper" qualified cryptographic signatures, but that's not the usual flows people think of when DocuSign is mentioned)