You will get ten "fun" visits. Note that buying a NE ticket tends to be worthwhiile if it will either (a) cover two or more complete trips, or (b) you will be "chaining" NE tickets. And it is more than 12 months from the start date of your first trip to the end date of the last planned trip.
This post includes the assumption you have a ten day MYW ticket with both the Park Hopper and Water Park Fun and More (WPF&M) options.
Hopefully this will make it a little clearer. In effect you have two tickets with different privileges on one card. Everything expires 14 days after first use unless you have the no-expire (NE) option. If you have the NE option all the entitlements are good until they are used up. Even if you use up all your major park days, the WPF&M entries remain valid until used. (Note you do not have to use the days consecutively.)
You have ten days of access to the four major parks (AK, DHS, EC, MK), and may visit more than one major park on a single day without any extra charges. Without the Park Hopper option you can only go to one major park per day.
You have ten entries to the minor parks (BB, DQ, OT, TL, WWS). These may or may not be used on the same days as you go to the major parks. However, if you went to TL in the morning, Oak Trail* in the afternoon, and Disney Quest in the evening of one day you would have used three of the ten entries. (Note that leaving and returning to the same minor park on the same day does not use an extra entry.)
If you go to minor parks only on one day and do not go to a major park you do not use up one of your major park days.
If you were to go to a Water Park in the morning and then one of the major parks for the remainder of the day you would have used one minor park entry and one day of major park entry.
Note that with the MYW ticket unless you have the hopper option you can only go to one major park per day. Unless you have the WPF&M option you cannot go to a minor park without upgrading or purchasing a separate ticket.
*Oak Trail is a nine-hole "Executive" walking (no carts) golf course. Each person must have their own set of clubs and they can be rented for $15 per person if they don't bring their own.
