A contract is an agreement to act in a specific way between two or more parties. The law generally sees performance of a contract as a duty. Simplest example is a buying/sellling contract: You go into a bakery because you want to buy bread; the baker displays bread he wants to sell. In agreeing to pay 2 EURO for 1/2 of bread, you conclude a contract. In paying it (you) and handing over the bread (the baker), the contract is fulfilled. On-line contracts/ e-Contracts (e.g. Amazone book store buying) are valid contracts.

www.weblaw.co.uk, a UK lawform, gives an overview on concluding on-line contracts and provides agreement templates, some free of charge (e.g. link agreement, non-disclosure agreement, software licence agreement etc.) 

Related legal Wiki articles:
e-invoicing
e-signature
e-payments
e-money
e-banking
Trust
Alternative Dispute Resolution (ADR) - in case either party does not comply with the contract duties

e-contracts in Portugal, see blogs:
Contratação sem intervenção humana
Online contract
Contratação electrónica - informações prévias
Contratação eletrónica - princípio da liberdade de celebração
Contratação eletrónica - Âmbito

In the USA:
Electronic Signature Law in the U.S
Contract law developments in the US