Die Wippe im Park ist heute frei.

Because Wippe is a feminine noun in German. Its basic dictionary form is die Wippe.

That affects:

• the article: die Wippe
• pronouns you might use later: sie for the seesaw

This is something you usually have to learn together with the noun:

• die Wippe = the seesaw

Im is a contraction of in dem.

So:

• in dem Park → im Park

Here it means in the park.

Grammatically, dem is dative case, because in can take different cases, and here it describes location rather than movement.

Compare:

• im Park = in the park / located in the park
• in den Park = into the park / moving into the park

In a normal German main clause, the finite verb goes in second position.

So in:

• Die Wippe | ist | heute frei

the verb ist is the second element.

This is one of the most important German word order rules.

You can also move another element to the front, but the verb still stays second:

• Heute ist die Wippe im Park frei.
• Im Park ist die Wippe heute frei.

Here frei means something like:

• free
• available
• not being used
• unoccupied

So Die Wippe im Park ist heute frei means the seesaw is available today.

German frei can have several meanings depending on context, for example:

• Ich habe heute frei. = I have the day off today.
• Der Platz ist frei. = The seat/space is free.
• Der Eintritt ist frei. = Admission is free.

Because here frei comes after the verb ist and works as a predicate adjective.

In German:

• adjectives before a noun usually take endings
• adjectives after sein, werden, bleiben, etc. usually do not

Compare:

• die freie Wippe = the free/available seesaw
• Die Wippe ist frei. = The seesaw is free/available

So frei stays in its basic form here.

Heute means today and acts as a time adverb.

It tells you when the seesaw is free.

German often places time words quite naturally in the middle of the sentence:

• Die Wippe im Park ist heute frei.

But heute can also be moved for emphasis:

• Heute ist die Wippe im Park frei.

That sounds perfectly normal too.

It most naturally identifies which seesaw we are talking about: the seesaw in the park.

So the sentence is understood as:

• The seesaw in the park is free today.

It also gives location, of course, but in this sentence it mainly helps specify the noun Wippe.

Yes, that is grammatically possible, but it sounds a little less natural in many contexts.

• Die Wippe im Park ist heute frei.
  This most naturally means the seesaw in the park is free today.

• Die Wippe ist heute im Park frei.
  This puts im Park later and can sound like you are emphasizing where it is free.

German word order often lets you shift emphasis by moving parts around, even when the basic meaning stays similar.

Wippe is a normal and standard German word for a playground seesaw.

Depending on region or context, people may also use:

• die Wippe
• sometimes more specifically die Schaukelwippe

But for a learner, die Wippe is the most useful everyday word.

There actually is an article there, just hidden inside im.

• im = in dem
• dem is the article

So im Park already includes the:

• im Park = in the park

That is why you do not see a separate word like der Park here.