The phrase “provided that” has numerous possible meanings, which can result in ambiguity if it is not used properly.

First of all, “provided that” can simply be a verb + conjunction combination. This is a common structure in legal writing. E.g.:

Section 3 provides that the obligation does not apply in the following circumstances.
(i.e. In accordance with section 3, the obligation does not apply…)

Before it was amended, the Act provided that the seller could take possession of the goods and retain them until payment was made.
(i.e. Under the previous version of the Act, the seller could take possession…)

In this way contracts, laws or acts have “provisions”. Provisions are particular rules, requirements, stipulations, etc.

“Provided that” also has an idiomatic meaning as a phrase that introduces a proviso. A proviso can be a number of things, including a condition, an exception and a qualification.

1) The most common idiomatic meaning is “on the condition that”. This is how “provided that” is usually understood in everyday English. Here are some examples:

You may go to the party provided that you’re home by 12.00.

You can drive a car provided that you have a valid licence.

You may produce your own version of the form, provided that the content is the same as in the attached template.

If you omit “that” the meaning stays the same:

You can drive a car provided you have a valid licence.

2) A less common meaning is “with the exception that”.  This meaning is rarely used outside of legal writing. E.g.:

If the Deposit is not paid, the Seller has the right to rescind this Agreement by delivering written notice to the Purchaser within 30 days of the date of this Agreement, provided that such rescission right is not effective if the Seller has rescinded the Preliminary Agreement for the Property.
(i.e. If the Deposit is not paid the Seller has the right to rescind this Agreement except if the Seller has already rescinded the Preliminary Agreement.)

All the above comments apply to the Properties, provided that the comments concerning the Expropriation Decision do not apply as there was no equivalent for the Properties.
(i.e. All the above comments apply to the Properties except the comments concerning the Expropriation Decision.)

3) Here’s an – admittedly rather complex – example of “provided that” as a qualification. Again this usage is only likely to appear in legal writing.

If the Seller’s production of the product is stopped or disrupted by an event of force majeure, the Seller must allocate its available supplies of the product to the Buyer based upon the same percentage of the Seller’s preceding year’s shipments of products to the Buyer in relation to the Seller’s total shipments of the product, provided, however, that to the extent that the Seller does not need any tonnage that is available in excess of the allocation of products to the Buyer, it must make that tonnage available to the Buyer.*
(i.e. The proviso qualifies the Seller’s obligation by adding additional information: If the Seller has a greater amount of the product available than the same percentage of the previous year’s shipments to the Buyer, he must also sell that amount to the Buyer.)

The phrase “providing that” is sometimes used as an alternative to “provided that”. Both mean the same thing and both are correct, but “provided that” is the more popular alternative.

* Example taken from Bryan Garner “Legal Writing in Plain English”, p. 111. Needless to say, Garner presents this sentence as an example of how NOT to write legal English. Garner generally does not advocate the use of provisos. He suggests rewriting and simplifying such sentences – a point of view that you might agree with if you’ve had difficulty understanding the last three examples in this post.