user7521: A lot of times my sibling and I have played chess and have ended up with just two kings. We have never known what would happen next. Two kings on the board would somehow result in an infinite game, as each can move forever wheresoever they like Hence, in such situations, is the game cancelled, tied, or withdrawn?

user3819: It is a draw (tie) because of "insufficient mating material". The game ends in this state.
The condition also arises when both sides are down to King+Bishop or King+Knight with no pawns on the board.

user2871: This is covered in FIDE's Laws of Chess 5.2b)

The game is drawn when a position has arisen in which neither player can checkmate the opponent’s king with any series of legal moves. The game is said to end in a ‘dead position’. This immediately ends the game, provided that the move producing the position was in accordance with Article 3 and Articles 4.2 – 4.7.

The term "insufficient mating material" describes this situation informally. However, the term "dead position" also applies to e.g. this kind of position:
[fen "8/6k1/8/p2p2p1/P2P2P1/8/1K6/8 w - - 0 1"]

Even with worst opposition, neither side can make any advances here, because the kings cannot cross the line set by the pawns. Therefore, this is an immediate draw by the same rule.

7521: <p>A lot of times my sibling and I have played chess and have ended up with just two kings. We have never known what would happen next. Two kings on the board would somehow result in an infinite game, as each can move forever wheresoever they like Hence, in such situations, is the game cancelled, tied, or withdrawn?</p>
 3819: <p>It is a draw (tie) because of "insufficient mating material". The game ends in this state.</p>

<p>The condition also arises when both sides are down to King+Bishop or King+Knight with no pawns on the board.</p>
 2871: <p>This is covered in FIDE's Laws of Chess 5.2b)</p>

<blockquote>
  <p>The game is drawn when a position has arisen in which neither player can checkmate the opponent’s king with any series of legal moves. The game is said to end in a ‘dead position’. This immediately ends the game, provided that the move producing the position was in accordance with Article 3 and Articles 4.2 – 4.7.</p>
</blockquote>

<p>The term "insufficient mating material" describes this situation informally. However, the term "dead position" also applies to e.g. this kind of position:</p>

<pre><code>[fen "8/6k1/8/p2p2p1/P2P2P1/8/1K6/8 w - - 0 1"]
</code></pre>

<p>Even with worst opposition, neither side can make any advances here, because the kings cannot cross the line set by the pawns. Therefore, this is an immediate draw by the same rule.</p>
