Can someone help me with the actual meaning of this statement. I am
confused as to how the values more than 2^64 are stored in the
computer memory.
Your questions is related with more generic concepts in Computer Science. For this question Javascript stays at higher level.
Please understand basic concepts for memory and storage first;
Also for Javascript please see this ECMAScript section
Ref: https://www.ecma-international.org/ecma-262/5.1/#sec-8.5
The Number type has exactly 18437736874454810627 (that is, 264−253+3) values, representing the double-precision 64-bit format IEEE 754 values as specified in the IEEE Standard for Binary Floating-Point Arithmetic, except that the 9007199254740990 (that is, 253−2) distinct “Not-a-Number” values of the IEEE Standard are represented in ECMAScript as a single special NaN value. (Note that the NaN value is produced by the program expression NaN.) In some implementations, external code might be able to detect a difference between various Not-a-Number values, but such behaviour is implementation-dependent; to ECMAScript code, all NaN values are indistinguishable from each other.
There are two other special values, called positive Infinity and negative Infinity. For brevity, these values are also referred to for expository purposes by the symbols +∞ and −∞, respectively. (Note that these two infinite Number values are produced by the program expressions +Infinity (or simply Infinity) and -Infinity.)
The other 18437736874454810624 (that is, 264−253) values are called the finite numbers. Half of these are positive numbers and half are negative numbers; for every finite positive Number value there is a corresponding negative value having the same magnitude.
Note that there is both a positive zero and a negative zero. For brevity, these values are also referred to for expository purposes by the symbols +0 and −0, respectively. (Note that these two different zero Number values are produced by the program expressions +0 (or simply 0) and -0.)
The 18437736874454810622 (that is, 264−253−2) finite nonzero values are of two kinds:
18428729675200069632 (that is, 264−254) of them are normalised, having the form
s × m × 2e
where s is +1 or −1, m is a positive integer less than 253 but not less than 252, and e is an integer ranging from −1074 to 971, inclusive.
The remaining 9007199254740990 (that is, 253−2) values are denormalised, having the form
s × m × 2e
where s is +1 or −1, m is a positive integer less than 252, and e is −1074.
Note that all the positive and negative integers whose magnitude is no greater than 253 are representable in the Number type (indeed, the integer 0 has two representations, +0 and -0).
A finite number has an odd significand if it is nonzero and the integer m used to express it (in one of the two forms shown above) is odd. Otherwise, it has an even significand.
In this specification, the phrase “the Number value for x” where x represents an exact nonzero real mathematical quantity (which might even be an irrational number such as π) means a Number value chosen in the following manner. Consider the set of all finite values of the Number type, with −0 removed and with two additional values added to it that are not representable in the Number type, namely 21024 (which is +1 × 253 × 2971) and −21024 (which is −1 × 253 × 2971). Choose the member of this set that is closest in value to x. If two values of the set are equally close, then the one with an even significand is chosen; for this purpose, the two extra values 21024 and −21024 are considered to have even significands. Finally, if 21024 was chosen, replace it with +∞; if −21024 was chosen, replace it with −∞; if +0 was chosen, replace it with −0 if and only if x is less than zero; any other chosen value is used unchanged. The result is the Number value for x. (This procedure corresponds exactly to the behaviour of the IEEE 754 “round to nearest” mode.)
Some ECMAScript operators deal only with integers in the range −231 through 231−1, inclusive, or in the range 0 through 232−1, inclusive. These operators accept any value of the Number type but first convert each such value to one of 232 integer values. See the descriptions of the ToInt32 and ToUint32 operators in 9.5 and 9.6, respectively.
